Currents in the Compressible and Incompressible Regions of the 2DEG

Abstract

We derive a general expression for the low-temperature current distribution in a two-dimensional electron gas, subjected to a perpendicular magnetic field and in a confining potential that varies slowly on the scale of the magnetic length l. The analysis is based on a self-consistent one-electron description, such as the Hartree or standard Kohn-Sham equations. Our expression, which correctly describes the current distribution on scales larger than l, has two components: One is an ``edge current'' which is proportional to the local density gradient and the other is a ``bulk current'' which is proportional to the gradient of the confining potential. The direction of these currents generally displays a striking alternating pattern.

27 pages in Tex, 4 figures available by request to [email protected], to appear in PRB

References in corpus (4)

• Sharp and Smooth Boundaries of Quantum Hall Liquids
• Composite Edge States in the $\nu =2/3$ Fractional Quantum Hall Regime
• Phase Separation of Edge States in the Integer Quantum Hall Regime
• Mesoscopic transport beyond linear response

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